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If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1), where 2p – 1 is a prime number}.Write Y in the roaster form.

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प्रश्न

If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1), where 2p – 1 is a prime number}.Write Y in the roaster form.

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उत्तर

If 2p − 1 is a prime number, then its only positive factors are:

1 and 2p − 1

This is because prime numbers have exactly two positive factors: 1 and itself.

Let’s say p = 5, then:

25 − 1 = 32 − 1 = 31

31 is a prime number, so the factors of 31 are {1, 31}

Y = {1, 2p - 1}

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अध्याय 1: Sets - Exercise [पृष्ठ १३]

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